Question

A wildlife researcher is tracking a flock of geese. the geese fly 3.5 km due west, then turn toward the north by 40 ∘ and fly another 4.5 km, what is the magnitude of their displacement

Answer 1

To solve this problem, we can use the cosine formula for calculating the length of the displacement:

c^2 = a^2 + b^2 – 2 a b cos θ

 

where c is the displacement, a = 3.5 km, b = 4.5 km, and θ is the angle inside the triangle

 

Since the geeze turned 40° from west to north, so the angle inside the triangle must be:

θ = 180 – 40 = 140°

 

c^2 = 3.5^2 + 4.5^2 – 2 (3.5) (4.5) cos 140

c^2 = 56.63

c = 7.53 km

 

So the magnitude of the displacement is 7.53 km

Answer 2

The magnitude of their displacement is 7.5 km

Further explanation

Vector is a quantity that has a magnitude and direction.

A vector in a cartesian coordinate is represented by an arrow in which the slope of the arrow shows the direction of the vector and the length of the arrow shows the magnitude of the vector.

A position vector of a point is a vector drawn from the base point of the coordinates O (0,0) to that point.

The addition of two vectors can be done in the following ways:

$\overrightarrow {AB} + \overrightarrow {BC} = \overrightarrow {AC}$

A negative vector is a vector with the same magnitude but in opposite direction.

$\overrightarrow {AB} = -\overrightarrow {BA}$

Let's tackle the problem!

First, let's look at the picture in the attachment!

Let:

$\overrightarrow{d_1} = -3.5 \widehat{i}$

$\overrightarrow{d_2} = -(4.5 \cos 40^o) \widehat{i} + (4.5 \sin 40^o) \widehat{j}$

Then:

$\overrightarrow{d} = \overrightarrow{d_1} + \overrightarrow{d_2}$

$\overrightarrow{d} = -3.5 \widehat{i} + -(4.5 \cos 40^o) \widehat{i} + (4.5 \sin 40^o) \widehat{j}$

$\overrightarrow{d} = -(3.5 + 4.5 \cos 40^o)\widehat{i} + (4.5 \sin 40^o) \widehat{j}$

$|\overrightarrow{d}| = \sqrt{ (3.5 + 4.5 \cos 40^o)^2 + (4.5 \sin 40^o)^2}$

$|\overrightarrow{d}| \approx 7.5 ~ km$

Learn more

• Velocity of Runner : brainly.com/question/3813437

• Kinetic Energy : brainly.com/question/692781

• Acceleration : brainly.com/question/2283922

• The Speed of Car : brainly.com/question/568302
• Magnitude of A Vector : brainly.com/question/2678571

Answer details

Grade: High School

Subject: Physics

Chapter: Vectors

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate , Vector , Scalar